Effect of thermal gradient on frequencies of an orthotropic rectangular plate whose thickness varies in two directions

A simple model is presented for the use of research workers in space technology, mechanical sciences and nuclear energy where certain components of the structures have to operate under elevated temperatures. The effect of a constant thermal gradient on the free vibrations of an orthotropic rectangular plate whose thickness varies linearly in two directions is considered. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz techniques with a two-term deflection function. The upper bound on the frequency corresponding to the first mode of vibrations is obtained for various boundary conditions, and for various values of the length to width ratio, two paper constants and the temperature gradient.